The estimation of heterogeneous treatment effects in the potential outcome setting is biased when there exists model misspecification or unobserved confounding. As these biases are unobservable, what model to use when remains a critical open question. In this paper, we propose a novel Bayesian methodology to mitigate misspecification and improve estimation via a synthesis of multiple causal estimates, which we call Bayesian causal synthesis. Our development is built upon identifying a synthesis function that correctly specifies the heterogeneous treatment effect under no unobserved confounding, and achieves the irreducible bias under unobserved confounding. We show that our proposed method results in consistent estimates of the heterogeneous treatment effect; either with no bias or with irreducible bias. We provide a computational algorithm for fast posterior sampling. Several benchmark simulations and an empirical study highlight the efficacy of the proposed approach compared to existing methodologies, providing improved point and density estimation of the heterogeneous treatment effect, even under unobserved confounding.

翻译：在潜在结果设定下，当存在模型误设或未观测混杂时，异质性处理效应的估计会产生偏差。由于这些偏差不可观测，何时使用何种模型仍是一个关键开放问题。本文提出了一种新颖的贝叶斯方法，通过综合多个因果估计值来减轻误设并改进估计，我们称之为贝叶斯因果合成。我们的方法建立在识别一个合成函数的基础上，该函数在不存在未观测混杂时能正确指定异质性处理效应，并在存在未观测混杂时实现不可约偏差。我们证明，所提方法能得到异质性处理效应的一致估计，要么无偏，要么具有不可约偏差。我们提供了一个用于快速后验抽样的计算算法。多项基准模拟研究和一项实证分析凸显了所提方法较现有方法的有效性，即使在未观测混杂下也能提供异质性处理效应的改进点估计和密度估计。